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Harmonics

Main Concept

Standing waves are waves that remain in a constant position but have a changing amplitude. They can result from the interference of waves traveling in different directions through a medium. A random stress applied to the object will produce many different waves, but only those waves with certain wavelengths will persist as standing waves.

 

The corresponding frequencies are called the natural frequencies of the object.

 

The fundamental frequency is the lowest frequency in which a standing wave pattern can form in a one dimensional medium.

 

Higher harmonics are multiples of the fundamental frequency.

 

The equations below govern the standing waves created in three different types of pipes filled with air.

Length of pipe

Wavelength

Frequencies

Closed-Closed pipe

L = n2λ

λ = 2Ln

f = n v2L

where

n  = Harmonic (positive integer)

L = Length of the pipe (m)

v  = Speed of sound in air (m/s)

Open-Open Pipes

L = n2λ

λ = 2Ln

 f= n v2L

where

n  = Harmonic (positive integer)

L = Length of the pipe (m)

v  = Speed of sound in air (m/s)

Closed-Open Pipes

L = n4λ

λ = 4Ln

f = n  v4L

where

n  = Harmonic (odd positive integer)

L = Length of the pipe (m)

v  = Speed of sound in air (m/s)

harmonic=

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